Related papers: Comparison techniques on inert top cell attachment…
In this work we shall present a survey on problems and results on singular holomorphic foliations and Pfaff systems on complex manifolds assuming that these objects possess invariant analytic varieties. We will focus on recent results which…
Maxwell lattices are characterized by an equal number of degrees of freedom and constraints. A subset of them, dubbed topological lattices, are capable of localizing stress and deformation on opposing edges, displaying a polarized…
We study topological properties of one-dimensional non-Hermitian systems without chiral symmetry and give phase diagrams characterized by topological invariants $\nu_E$ and $\nu_{total}$, associated with complex energy vorticity and…
We show Poincar\'e Duality for $\mathbf{F}_p$-\'etale cohomology of a smooth proper rigid-analytic space over a non-archimedean field $K$ of mixed characteristic $(0, p)$. It positively answers the question raised by P. Scholze in [Sch13a].…
We prove conditions under which the total space of the pullback of a sphere fibration over a connected sum is homotopy equivalent to a connected sum with a gyration. Existing results of this type often depend on geometric methods. We…
We obtain new invariants of topological link concordance and homology cobordism of 3-manifolds from Hirzebruch-type intersection form defects of towers of iterated p-covers. Our invariants can extract geometric information from an arbitrary…
There appeared not long ago a Reduction Formula for derived Hochschild cohomology, that has been useful e.g., in the study of Gorenstein maps and of rigidity w.r.t. semidualizing complexes. The formula involves the relative dualizing…
For a hypersurface V of a conformal space, we introduce a conformal differential invariant I = h^2/g, where g and h are the first and the second fundamental forms of V connected by the apolarity condition. This invariant is called the…
In this paper, we consider an equivalence problem of second order partially differential equations (PDE) and a duality of the flat differential equation. For the equivalence problem, explicit form of invariants (curvatures) are given. We…
We classify in terms of Hopf-type properties mapping tori of residually finite Poincar\'e Duality groups with non-zero Euler characteristic. This generalises and gives a new proof of the analogous classification for fibered 3-manifolds.…
In this paper we analyze some relationships between the topological complexity of a space $X$ and the category of $C_{\Delta_X},$ the homotopy cofibre of the diagonal map $\Delta_X:X\rightarrow X\times X.$ We establish the equality of the…
Real Bruhat cells give an important and well studied stratification of such spaces as $GL_{n+1}$, $Flag_{n+1} = SL_{n+1}/B$, $SO_{n+1}$ and $Spin_{n+1}$. We study the intersections of a top dimensional cell with another cell (for another…
In a non-compact setting, the notion of hyperbolicity, and the associated structure of stable and unstable manifolds (for unbounded orbits), is highly dependent on the choice of metric used to define it. We consider the simplest version of…
Equations of a heavy rotating body with one fixed point can be deduced starting from a variational problem with holonomic constraints. When applying this formalism to the particular case of a Lagrange top, in the formulation with a diagonal…
This paper presents tractable reformulations of topology optimization problems of structures subject to frictionless unilateral contact conditions. Specifically, we consider stiffness maximization problems of trusses and continua. Based on…
A new linear system is constructed for Poincar\'e supergravities in two dimensions. In contrast to previous results, which were based on the conformal gauge, this linear system involves the topological world sheet degrees of freedom (the…
This is a slightly corrected version of the article published by Functional Analysis and its Applications in 1993. We define the quadratic duality for algebras with nonhomogeneous relations; the duality between the algebra of differential…
This article is a survey of algebra in the $\infty$-categorical context, as developed by Lurie in "Higher Algebra", and is a chapter in the "Handbook of Homotopy Theory". We begin by introducing symmetric monoidal stable…
In this note, we study the connection between Gray tensor product and suspension. We derive a characterization of weak equivalences as fully faithful and essentially surjective functors. We construct the $co$ duality, a weak involution that…
The simplices and the complexes arsing form the grading of the fundamental (desymmetrized) domain of arithmetical groups and non-arithmetical groups, as well as their extended (symmetrized) ones are described also for oriented manifolds in…